Solution and stability of continuous-time cross-dimensional linear systems

We investigate the solution and stability of continuous-time cross-dimensional linear systems(CCDLSs)with dimension bounded by V-addition and V-product.Using the integral iteration method,the solution to CCDLSs can be obtained.Based on the new algebraic expression of the solution and the Jordan decomposition method of matrix,a necessary and sufficient condition is derived for judging whether a CCDLS is asymptotically stable with a given initial state.This condition demonstrates a method for finding the domain of attraction and its relationships.Then,all the initial states that can be stabilized are studied,and a method for designing the corresponding controller is proposed.Two examples are presented to illustrate the validity of the theoretical results.